Guided Discrete Diffusion for Constraint Satisfaction Problems

AI for constraint satisfaction problems is an important field researched for more than half a century. Sudoku, a puzzle where no row, column, or block can have two of the same number, is a popular benchmark to assess the ability of models to reason over constraints. With the rise of deep learning, many deep neural networks have been used to solve sudoku, such as transformers and graph neural networks to name a few. These networks perform well but are trained under supervision and assume access to a labelled dataset. Given the importance of identifying patterns in the structure of Sudoku solutions, these supervised methods may be limited in their capability to generalize to unseen puzzles (as combinatorially many exist) or perform well under limited data settings-and at the minimum, require a supervised dataset of initial puzzles x to final puzzle solutions y.

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